The structural state of Fe-Pd-Au alloys has a significant effect on the physical properties and the character of the magnetic phase diagrams. This occurs due to changes in the competing exchange interactions between atoms. Based on the data obtained by the Mössbauer spectroscopy, two models of the distribution of gold atoms in the unit cell LI2 as a function of the annealing temperature during ordering were proposed. The first model describes the structure of the alloy after high-temperature annealing (970 K) and assumes a statistical distribution of Au atoms over all faces of the LI2 type unit cell. The second model describes the structure of the alloy after low-temperature annealing (720 K) and assumes that Au atoms occupy only the central nodes of the face-centered lattice in the palladium sublattice LI2, so that the entire superstructure becomes anisotropic. Here we present the results of field ion microscopy studies on the occupancy of specific nodes in the unit cell by gold atoms in the ternary ordered alloy Fe25Pd50Au25 exhibited the LI2 superlattice. Field ion microscopy (FIM) is used to obtain data on the settlement of nodes with gold atoms in the LI2 superstructure. It is established that Au atoms are equally likely to occupy nodes of face-centered faces in the LI2 lattice, so that the entire superstructure becomes isotropic.